LONDON: Indian President Pratibha Patil is expected to meet Prime Minister Gordon Brown on day two Wednesday of her state visit to former colonial power Britain aimed in part at boosting trade links.

Patil received a red-carpet welcome from Queen Elizabeth II after becoming the first Indian head of state to visit Britain for almost 20 years.

The queen hosted a banquet Tuesday for Patil, the first Indian woman to be elected to the ceremonial role, at her Windsor Castle residence, where she is staying during the three-day trip.

The queen paid tribute at the dinner to the strong, historic ties between the two countries and the contribution of India's population in Britain.

"Britain and India have a long shared history which today is a source of great strength in building a new partnership fit for this new century," she said in a speech to the 148 guests who included Brown, senior royals, Harry Potter author JK Rowling and leading members of Britain's Indian community.

The British monarch also remembered the Mumbai terrorist attacks that killed 166 people and injured more than 300 others last November.

"I would like to pay tribute to the courage and steadfastness shown by the Indian security forces and the people in the face of this great tragedy."

Patil, in her speech, highlighted the shared values of the two countries and praised the multi-cultural diversity of London.

She also invited the queen to visit New Delhi next year when the Indian capital hosts the Commonwealth Games.

"Your Majesty, the ties between India and the UK are built upon shared values and traditions. There are numerous commonalities between our two countries," Patil said.

"We are vibrant democracies with a free press and active civil societies, we both believe in freedom, dignity and respect."

Improving trade links and boosting British investment in India will be high on the agenda for the visit, which will include talks with Brown on Wednesday, Indian officials have said.

Britain is the biggest European investor in India and bilateral trade between the two countries was worth 12.6 billion pounds (20.7 billion dollars, 13.9 billion euros) in 2008, according to the Foreign Office in London.

The countries also cooperate closely on counter-terrorism, in particular sharing information on attacks on transport systems in London in 2005 and Mumbai, as well as climate change and non-proliferation.

Some 1.3 million Indians live in Britain, representing about two percent of the population, according to Foreign Office figures.

Patil, who arrived on Monday, will also join the queen on Thursday in launching the baton relay for the Commonwealth Games.

The relay will start at Buckingham Palace in London and travel through 70 countries before reaching the Indian capital when the games open on October 3 next year.

Patil will also visit Cyprus before returning home on Saturday.